Is it allowed for a woman to enter the state of ihram in any clothing she wishes?

Yes, she may enter the ihram in whatever clothing she wishes. She does not have any specific type of clothing that she must wear for ihram as many of the general public think. But it is best for her to enter the ihram in clothing which is not beautiful and will not attract the one who sees it. This is because she is going to be mixing with men, so her clothing must not be such that it tempts the looker. It should not be beautiful but should be customary and not a temptation.